It is unclear whether other potential candidates, including Gov. Andy Besha and Transportation Secretary Pete Buttigieg, plan to meet with Ms. Harris.
Harris officially became the Democratic presidential nominee on Friday after the party's delegates voted.
Once Ms. Harris's running mate is announced, the two are expected to tour key battleground states.
Mr. Shapiro has enjoyed strong approval ratings since his election in 2022 and could help Harris carry Pennsylvania, a must-win state in the race for the White House.
Arizona Sen. Mark Kelly, a former Navy pilot and NASA astronaut, is a leading voice on gun safety, and his strong stance on the border and occasional criticism of the Biden administration could help him appeal to independents and conservative voters.
Mr. Walz, who served in Congress for 12 years before becoming Minnesota governor in 2019, gained national attention for his strategy of calling Donald Trump and J.D. Vance “odd.”
On Friday, President Joe Biden said he had talked to Ms. Harris about finding a running mate. Asked what qualities he looks for in a vice presidential candidate, he said, “I’ll let her figure it out.”
Potential partners to run alongside Ms. Harris as a Democratic candidate in November must go through a rigorous vetting process that includes answering up to 200 questions before being seriously considered.
Delegates do not have to vote for the vice presidential candidate.
